An Imperfect Production Model for Breakable Multi-Item with Dynamic Demand and Learning Effect on Rework over Random Planning Horizon

In recent times, in the literature of inventory management there exists a notorious interest in production-inventory models focused on imperfect production processes with a deterministic time horizon. Nevertheless, it is well-known that there is a high influence and impact caused by the learning effect on the production-inventory models in the random planning horizon. This research work formulates a mathematical model for a re-workable multi-item production-inventory system, in which the demand of the items depends on the accessible stock and selling revenue. The production-inventory model allows shortages and these are partial backlogged over a random planning horizon. Also, the learning effect on the rework policy, inflation, and the time value of money are considered. The main aim is to determine the optimum production rates that minimize the expected total cost of the multi-item production-inventory system. A numerical example is solved and a detailed sensitivity analysis is conducted in order to study the production-inventory model.

Two-player zero-sum stochastic differential games with random horizon

We consider a two-player zero-sum stochastic differential game with a random planning horizon and diffusive state variable dynamics. The random planning horizon is a function of a non-negative continuous random variable, which is assumed to be independent of the Brownian motion driving the state variable dynamics. We study this game using a combination of dynamic programming and viscosity solution techniques. Under some mild assumptions, we prove that the value of the game exists and is the unique viscosity solution of a certain nonlinear partial differential equation of Hamilton–Jacobi–Bellman–Isaacs type.

Optimal Production Planning for a Random Horizon

The article presents the mathematical model of production control for a random planning horizon. The model assumes that the horizon of control is unknown and connected with reliability of machines, which are used for production. The aim of the control model is to determine the number of products which should be manufactured in each planning period to minimize both manufacturing costs and potential financial penalties for failing to fulfill the order completely.